The Areolar Strain Approach For Grazing Waves
Author(s)
I. D. Kotchergenko
Abstract
Authors are almost unanimous regarding the ratios between reflected and
incident plane wave amplitudes obtained through the condition of zero traction at
a free surface, except for grazing waves. Goodier and Bishop showed that the
traditional approach fails in cases of wave travels grazing the surface. The writer
argues that the traditional theory fails also for incidence angles beyond that
where the total mode conversion from P-wave to S-wave occurs, and also shows
that after this angle, phase inversion no longer occurs. The reason for this
behavior is that plane waves are characterized by some constraints between their
fundamental modes of strain. These constraints are set up by the waveguide
equations presented by the writer. It then happens that it does not exist a set of
incident and reflected plane waves that can fulfils the condition of zero traction
at the reflecting surface. Therefore some scattering of the incident wave is
supposed to occur near the free boundary. The equation of conservation of flux
of energy together with the equations of zero traction at surface, are not
sufficient for determining the nature of this scattering. The writer hence appeals
also to the strain compatibility equation at the free surface and obtains an
expression for the reflecting P-wave that agrees with the results of Goodier and
Bishop. It is remarkable that the angle of total mode conversion is preserved.
New curves of reflections are proposed. The P-wave reflection curve little
differs from the traditional up to the total mode conversion angle but completely
differs between this up to the grazing angle. The S-wave to P-wave reflection
ratio almost follows the traditional.
Waves are represented through the superposition of the four fundamental
modes of the plane areolar strain theory of elasticity. This theory was presented
at WIT Transactions on Modeling and Simulation, Vol. 46, 2007, WIT Press,
(free), with application to orthotropic materials and finite rotations.
Keywords: elastic waves, wave reflection, waveguides, grazing waves.
Keywords
Keywords: elastic waves, wave reflection, waveguides, grazing waves.
Related Book
Other papers in this volume
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